Definition: To penetrate with or as if with a sharp-edged instrument or object; to make an opening, incision, or wound in (something) with a sharp-edged tool or object.
There are many ASL signs for CUT. Here are some examples, some using descriptive classifiers and/or locative classifiers.
A long narrow incision in the skin made by something sharp.
To cut something into slices (e.g. tomato, salami, etc.)
To cut something (e.g. paper) with scissors.
To cut or snip hair.
To cut nails (with a scissors). For cutting nails with a nailcutter, use a different classifier.